From a practical point of view, the development of calibrated-\(\delta \)  adjustment MI is motivated by the issue incomplete recording of ethnicity data in UK primary care electronic health records. Routine recording of ethnicity has been incorporated at the general practice level in the UK, and the variable is therefore available in many large primary care databases. However, research addressing ethnicity has been constrained by the low level of recording.[1]}, [2]}, [3]} Studies often handle missing data in ethnicity by either dropping ethnicity from the analysis [4]}, performing a complete record analysis (i.e. excluding individuals with missing data), or single imputation of missing values with the White ethnic group [5]}; these methods will generally lead to biased estimates of association and standard errors.[6]} In addition, the probability that ethnicity is recorded in primary care may well vary systematically by ethnic groups, even after adjusting for other variables.[3]} This implies a potential MNAR mechanism for ethnicity, and as a result, standard MI might fail to give valid inference for the underlying population. Since the population marginal distribution of ethnicity is available in the UK census data, the plausibility of the MAR assumption for ethnicity in UK primary care data can be assessed by using standard MI to handle missing data, and comparing the resulting ethnicity distribution to that in the census. In earlier work, we explored departures from the MAR assumption for other incomplete heath indicators by comparing the results with external nationally representative datasets.[8]}, [9]} As an example of this, Marston et al. (2014) reported that if smoking status is missing for a patient then he or she is typically either an ex-smoker or non-smoker, and accordingly proposed only allowing imputed data to take one of these two values [9]}. The method we describe here supersedes this ad-hoc approach, providing a way to incorporate population distribution information into MI.
